Gyroscopic systems considered here have the form Ay¨ + Gy˙ + Ky = 0 where A, G, K are real n × n matrices with A > O, GT = −G, KT = K, and the stiffness matrix K has some negative eigenvalues; i.e., the equilibrium position is unstable (when G = 0). A new necessary condition for stability is established. It is also shown that gyroscopic systems with K < 0 and G singular are always unstable for G sufficiently large.

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